New insights in GMRES-like methods with variable preconditioners

In this paper we compare two recently proposed methods, FGMRES (Saad, 1993) and GMRESR (van der Vorst and Vuik, 1994), for the iterative solution of sparse linear systems with an unsymmetric nonsingular matrix. Both methods compute minimal residual approximations using preconditioners, which may be different from step to step. The insights resulting from this comparison lead to better variants of both methods.